Rule of 78

Detailed Definition

The Rule of 78, also known as the Sum-of-the-Digits Method, is a formula used to allocate interest across the term of a loan that has upfront interest (known as add-on interest). The “78” refers to the sum of the digits of a 12-month period (1+2+3+…+12 = 78). This rule favors lenders and tends to impose more interest cost on borrowers who pay off loans early.

Examples

Example 1:

Imagine a 12-month loan where the principal amount is $1,000 with an 8% add-on interest rate.

Interest = $1,000 * 0.08 = $80
Total repayment amount = $1,000 + $80 = $1,080.
Monthly payment = $1,080 / 12 = $90.

If the borrower prepays at the end of the 1st month:
- Interest proportion for 1st month = 12/78 of $80 = $12.31.
- Repaid principal proportion = Monthly Payment ($90) - Earned Interest ($12.31) = $77.69.
- Total paid principal after 1st month = $77.69.
- Remaining balance = $1,000 Principal – $77.69 = $922.31.

Example 2:

If the borrower prepays at the end of the 11th month (and interest has almost been fully paid):

Interest proportion up to the 11th month = Sum of digits from 1 to 11 = 66/78 of $80 ≈ $67.69.
Remaining interest to be refunded = $80 - $67.69 = $12.31.

Frequently Asked Questions

Q1: What does the Rule of 78 benefit?

A1: The Rule of 78 benefits the lender because it collects more interest in the earlier months of the loan.

Q2: Can the Rule of 78 be applied to all types of loans?

A2: No, the Rule of 78 is primarily used for fixed-rate installment loans with add-on interest. It’s less common in modern-day amortized loans.

Q3: Is the Rule of 78 legal in all states?

A3: No, the application of the Rule of 78 is regulated and prohibited in some states for certain types of loans.

Q4: Can I avoid the Rule of 78 penalties?

A4: Understanding the loan contract and consulting with legal/financial advisors or avoiding such loans can help mitigate these penalties.

Q5: How is the Rule of 78 different from simple interest?

A5: The Rule of 78 front loads interest payments, while simple interest is calculated evenly over the loan term.

Add-On Interest: Interest which is calculated upfront based on the original loan amount.
Amortization: The process of spreading the loan payments consisting of interest and principal over time.
APR (Annual Percentage Rate): The annual rate charged for borrowing.
Prepayment Penalty: A fee imposed by lenders if a borrower pays off a loan before its due period.

Online Resources

References

Ross, Stephen A., Randolph W. Westerfield, and Jeffrey Jaffe. Corporate Finance, 11th edition, McGraw-Hill Education.
Brigham, Eugene F., and Michael C. Ehrhardt. Financial Management: Theory & Practice, 15th Edition, Cengage.

Suggested Books for Further Study

“Principles of Corporate Finance” by Richard A. Brealey, Stewart C. Myers, and Franklin Allen.
“Financial Management: Theory & Practice” by Eugene F. Brigham and Michael C. Ehrhardt.
“Essentials of Corporate Finance” by Stephen A. Ross, Randolph W. Westerfield, and Bradford D. Jordan.

Real Estate Basics: Rule of 78 Fundamentals Quiz

### The Rule of 78 is most commonly applied to: - [ ] Mortgages - [ ] Revolving Credit - [ ] Installment Loans - [x] Add-On Interest Loans > **Explanation:** The Rule of 78 is mainly applied to installment loans with add-on interest, calculating interest more heavily towards the earlier months. ### Why is the sum 78 used in the Rule of 78 calculations? - [ ] It represents the total monthly payment. - [ ] It's a traditional lender fee. - [x] It is the sum of the digits from 1 to 12. - [ ] It has no real significance. > **Explanation:** The sum 78 comes from adding up the digits from 1 to 12. ### Who benefits more from the Rule of 78? - [ ] The borrower - [x] The lender - [ ] Both equally - [ ] Neither > **Explanation:** The lender benefits more, as they receive a larger portion of the loan interest in the early payments. ### Can the Rule of 78 be used for mortgages? - [ ] Yes - [x] No - [ ] Sometimes - [ ] Only with certain conditions > **Explanation:** Typically, the Rule of 78 is not used for mortgages but for fixed-rate installment loans with add-on interest. ### Early repayment of the loan under the Rule of 78 is a disadvantage to whom? - [x] The borrower - [ ] The lender - [ ] Both parties - [ ] It cannot be prepaid. > **Explanation:** Early repayment disadvantages the borrower as they pay more interest in the initial period. ### What percentage of the total interest is charged by the second month according to the Rule of 78? - [ ] 1/78 - [ ] 2/78 - [x] 23/78 - [ ] 1/12 > **Explanation:** By the second month, the fraction would be (12+11)/78. ### Is the Rule of 78 legal for all types of loans in every U.S. state? - [ ] Yes - [ ] No, it varies by loan type - [x] No, it varies by state - [ ] Yes, but only for variable rate loans > **Explanation:** The legality of the Rule of 78 varies by state, with some states prohibiting its use for certain loan types. ### What do you call the interest calculated upfront based on a loan's original amount? - [x] Add-On Interest - [ ] Simple Interest - [ ] Compound Interest - [ ] Variable Interest > **Explanation:** Add-On Interest is calculated upfront. ### Does responsible lending practices affect the application of Rule of 78? - [x] Yes - [ ] No - [ ] Only in certain cases - [ ] It never does > **Explanation:** Responsible lending often impacts the application, and some states have regulations that restrict or prohibit its use. ### If the borrower makes payments on time without prepayments, what happens to the Rule of 78 interest allocation? - [ ] It remains irrelevant - [x] Interest is distributed heavier in beginning periods. - [ ] It adjusts evenly over time. - [ ] There’s no specific impact. > **Explanation:** The allocation favors early interest collection which applies the rule more noticeably in the beginning periods.